Heat olive oil in a large skillet or wok over medium-high heat. Add chicken pieces, season with salt and pepper, and cook until and nearly cooked through,
Turn up the heat to high and add garlic, ginger, broccoli, bell peppers, and carrot to the skillet. Stir-fry for about 3 to 4 minutes until vegetables are just tender.
Pour the sauce over the chicken and vegetables. Stir well to combine and continue to cook for another 2 to 3 minutes or until the sauce has thickened and the chicken is cooked through.